Question Video: Finding the Length of the Altitude in a Right Triangle given the Triangle’s Dimensions | Nagwa Question Video: Finding the Length of the Altitude in a Right Triangle given the Triangle’s Dimensions | Nagwa

# Question Video: Finding the Length of the Altitude in a Right Triangle given the Triangleβs Dimensions Mathematics

Determine the length of line segment π΄π·.

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### Video Transcript

Determine the length of line segment π΄π·.

We note that π· is the projection of π΄ onto the line π΅πΆ and that the triangle π΄π΅πΆ is a right triangle at π΄. And we recall that the corollary to the Euclidean theorem, that is, the altitude rule, tells us that π΄π· squared is equal to π΅π· multiplied by πΆπ·. This tells us that the altitude or height of the right triangle squared is the product of the lengths of the segments of the hypotenuse when it is split by the altitude.

Weβre given that the two segments are 2.5 centimeters, thatβs πΆπ·, and 6.4 centimeters, thatβs π΅π·. And substituting these values in, we have π΄π· squared is 6.4 multiplied by 2.5. This evaluates to 16, so π΄π· squared is 16. Now, taking the square root on both sides of the equation, noting that π΄π· is a length and so is nonnegative, we get π΄π· is the square root of 16, which is four. The length of π΄π· is therefore four centimeters.